Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A NON-ITERATIVE RECONSTRUCTION METHOD FOR AN INVERSE PROBLEM MODELED BY A STOKES-BRINKMANN EQUATIONS

  • Hassine, Maatoug (Department of Mathematics Faculty of Sciences Avenue Monastir University) ;
  • Hrizi, Mourad (Department of Mathematics Faculty of Sciences Avenue Monastir University) ;
  • Malek, Rakia (Department of Mathematics Faculty of Sciences Avenue Monastir University)
  • Received : 2019.06.07
  • Accepted : 2020.05.14
  • Published : 2020.09.01
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Abstract

This work is concerned with a geometric inverse problem in fluid mechanics. The aim is to reconstruct an unknown obstacle immersed in a Newtonian and incompressible fluid flow from internal data. We assume that the fluid motion is governed by the Stokes-Brinkmann equations in the two dimensional case. We propose a simple and efficient reconstruction method based on the topological sensitivity concept. The geometric inverse problem is reformulated as a topology optimization one minimizing a least-square functional. The existence and stability of the optimization problem solution are discussed. A topological sensitivity analysis is derived with the help of a straightforward approach based on a penalization technique without using the classical truncation method. The theoretical results are exploited for building a non-iterative reconstruction algorithm. The unknown obstacle is reconstructed using a levelset curve of the topological gradient. The accuracy and the robustness of the proposed method are justified by some numerical examples.

Keywords

Acknowledgement

The second author would like to thank Professors Maria-Luisa Rapún for useful discussions.

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